A balloon behaves so that the pressure isP=C2V1/3 and C2 = 100 kPa/m. The balloon is blown up with air from a starting volume of 1 m3 to a volume of 4 m3. Find the final mass of air, assuming it is at 25◦C, and the work done by the air.

Explanation:

As it is given that,

As the system is not gaining or losing heat. So, it is an adiabatic process in an assumed ideal gas. The polytropic extent n is .

                       =

                        = 100 kpa

                      =

                      = 158.74 kpa

Now, work done by the air is as follows.

                       =

                       =

                       = 401.22 kJ

Work done by the air is as follows.

                           =

                           = 7.424 kg

Thus, we can conclude that final mass of air is 7.424 kg and work done by the air is 401.22 kJ.